Hose clamps with so-called "Oetiker" ears consisting of two generally outwardly extending leg portions interconnected by a bridging portion have enjoyed immense commercial success since almost five decades ago. These clamps originally included two ears and were made from tubular stock (U.S. Pat. No. 2,614,304). With the use of improved manufacturing techniques assuring better dimensional controls of the hose materials, clamps with only one ear became a practical reality. Additionally, clamps also were made from clamping band material of galvanized steel and stainless steel (U.S. Pat. No. 3,082,495). However, problems arose, especially when using thinner clamping band materials in the ability to properly realize the desired omega shape of the ear upon plastic deformation thereof with conventional pincer tools. More specifically, as disclosed in U.S. Pat. No. 3,402,436, in lieu of deforming into a more or less omega shape upon plastic deformation, the ears generally designated by reference numeral 20 in FIG. 1 of this application had a tendency to buckle as illustrated in this figure. Special tools with a hold-down member 50 (FIG. 2) were developed to counteract this tendency. Apart from the cost factor, the need for special tools detracted from the universal appeal of such hose clamps. As also disclosed in U.S. Pat. No. 3,402,436, the tendency to buckle was eliminated by the use of one or more reinforcing grooves 25 in the bridging portion of the "Oetiker" ear. These reinforcing grooves could be either in the form of pressed-out, deep-drawn embossments 25 (FIGS. 4-6) or in the form of pressed-out, deep-drawn indentations 25' (FIGS. 7 and 8). These reinforcements 25 and 25' were normally in the form of a narrow groove resembling the shape of a canoe with a pronounced curved bottom. As new hose materials became available which were made from thinner and much harder plastic materials and as the demands made of hose clamps also changed therewith, a new reinforcing arrangement of the bridging portion came into being as disclosed in U.S. Pat. No. 5,282,295. The improved reinforcement generally designated by reference numeral 125 in the bridging portion 122 of the ear generally designated by reference numeral 120 (FIGS. 9-12) had a relatively shallow pan-shaped depression including a generally flat bottom part 126 as well as longitudinal and transverse connecting portions 127 and 128 connecting the bottom part 126 with the remaining non-depressed bridging portion 122. The area of the bottom part was specified in this patent to be at least 35% of the original area of the non-reinforced bridging portion, and preferably between about 40% to about 60% thereof. This prior art reinforcing arrangement for the bridging portion has also proved commercially highly successful. However, because of material needs in the formation of the depression 125, the sides of this prior art bridging portion become curved concavely as also disclosed in this patent. Additionally, an important feature of the so-called "Oetiker" ears resides in the automatic compensation in case of thermal or pressure variations in the hose. This feature is due to the elastic behavior caused by stresses set up in the ear during plastic deformation which resist and compensate for changes in the shape of the plastically deformed ear. The plastically deformed "Oetiker" ear thereby compensates also for aging of the hose material in that it seeks to maintain the original clamping pressure as the external diameter of the hose decreases due to aging. It is therefore desirable to limit the anti-buckling reinforcing areas as much as possible to areas other than areas where compensating stresses are set up during plastic deformation of the normal flat band material including the areas of the connections between the bridging portion and the leg portions.